Exercise:
Berechne die folgen Bruchterme. nprvmulticols abclist abc dfracaa+b + abc dfracz^z+ - z abc -dfracmm-n abc dfrace^- abc badda+b+c abc baddx+yx-y-x-yx+y abc baddmm--m-m+ abc baddw-w-+w+w+ abc baddcc+d-c-dc+d abc badduu^+uv+v^-u+v abc baddx-yx+y+x+yx+y abc baddr+r^-r+r^+r^ abc baddcc-d-cdc^-d^ -dfracdc+d abc baddzz--z+-dfracz^-z- abc badda-ba+b+a+ba+b abc badduuv+v^-vu^+uv abc baddrx+ry+sx+sy abc baddz+z^--z+z^+z abc badd+-e abc baddr-r++-r^ abc badda-bc-d-a+bd-c abc baddss^-++s-s abc baddn-n--n+n+ + abc baddr-r--rr- - dfrac abc baddx-y-y-x -dfracx-y abc baddk+k-+k+k-+dfrack+-k abclist nprvmulticols

Solution:
abclist abc * dfracaa+b + fraca+a+ba+b fraca+ba+b * abc * dfracz^z+ - z fracz^-z^-zz+ frac-zz+ * abc * -dfracmm-n fracm-n-mm-n fracm-nm-n * abc * dfrace^- frace^-e^+ frac-e+ * abc * badda+b+c fraca+b+cac+bc * abc * baddx+yx-y-x-yx+y fracx+y^-x-y^x-yx+y fracx^+xy+y^-x^+xy-y^x^-y^ fracxyx^-y^ * abc * baddmm--m-m+ fracm^+m-m^+m-m-m+ fracm-m^+m- * abc * baddw-w-+w+w+ fracw-w+ +w+w-w-w+ fracw^-w-+w^+w-w^+w- fracw^+w-w^+w- * abc * baddcc+d-c-dc+d fracc-c+dc+d fracc+dc+d frac * abc * badduu^+uv+v^-u+v fracu-u-vu^+uv+v^ fracu-vu^+uv+v^ * abc * baddx-yx+y+x+yx+y fracx-yx+y + fracx+yx+y fracx-y+x+yx+y fracx+yx+y * abc * baddr+r^-r+r^+r^ fracr+r^-fracr+r^r+ fracr^+r+-r-r^r+ fracr^r^r+ fracr+ * abc * baddcc-d-cdc^-d^ -dfracdc+d fracc^+cd-cd-cd+d^c+dc-d fracc^-cd+d^c+dc-d fracc+d^c+dc-d fracc+dc-d * abc * baddzz--z+-dfracz^-z- fracz^+z-z+-z-z+ fracz^-z-z-z+ * abc * badda-ba+b+a+ba+b fraca-b + a + ba+b fraca+ba+b frac * abc * badduuv+v^-vu^+uv fracuvu+v - fracvuu+v fracu^-v^uvu+v fracu+vu-vuvu+v fracu-vuv * abc * baddrx+ry+sx+sy fracs+rrsx+rsy * abc * baddz+z^--z+z^+z fracz+z+z- - fracz+zz+ fracz^+z-z+z-zz+z- fracz^+z-z^-z+zz+z- fracz+zz+z- fracz^-z * abc * badd+-e frac-e * abc * baddr-r++-r^ fracr-r+ + frac-r+r fracr--r+-r+r fracr--r^+-r+r frac-r^+r+-r+r frac+r-r-r+r frac-r-r fracr-r- * abc * badda-bc-d-a+bd-c fraca-b+a+bc-d fracac-d * abc * baddss^-++s-s fracss+s- - frac+ss-  fracs-s+^s+s- fracs-s^-s-s+s- frac-s^+s-s+s- frac-s+^s+s- frac-s-s- * abc * baddn-n--n+n+ + fracn-n+-n+n-+n-n+n-n+ fracn^+n--n^-n++n^+n-n-n+ frac-n^-n-n^+n- * abc * baddr-r--rr- - dfrac baddr-r--rr- - dfrac fracr-r--rr--r-r-r-r- fracr^-r+-r^+r-r^+r-r-r- frac-r^-r+r-r- frac-r^-r+r-r- frac-r^-r+r^ -r+ * abc * baddx-y-y-x -dfracx-y fracx-y + fracx-y-fracx-y frac+-x-y fracx-y * abc * baddk+k-+k+k-+dfrack+-k frack+k- + frack+k- - frack+k- frack++k+-k-k- frack-k- frack-k-   frac * abclist